Devices and methods for performing vascular anastomosis. A needle passer is used to pass one or more needles through tissue to thread one or more lengths of suture through the tissue. The needle passer is operable using one hand and includes a handle supporting a shaft assembly carrying first and second sets of needles connected by lengths of suture. An actuator assembly uncovers the first set of needles, moves them into a radially extended position, and then passes them through tissue, for example, the wall of a patient's aorta. The needle passer may be pistol-shaped with a trigger that is moved in one direction to sequentially uncover, radially extend, and move the first set of needles through the aorta around an aortotomy. The needles may then be pulled away from the patient to thread the suture through the tissue. A delivery device is used to deliver a member adapted to be secure to body tissue, such as a vascular conduit. The delivery device includes a shaft and a collar mounted for relative movement. The shaft supports a vascular conduit so that an end of the conduit is disposed against the collar. A sealing element may be positioned on the collar beneath the end of the conduit. The needles in the second set are removed from the needle passer and are placed through the conduit and sealing element and into the collar. The shaft is then moved through the collar to move the vascular conduit along the suture into contact with the aorta. The delivery device is then removed and the respective ends of each suture length secured to fix the end of the vascular conduit to the aorta.